To accurately approximate sin.x and cos.x for inclusion in a mathematical library, we first restrict their domains. Given a real number x, divide by to obtain the relation |x] =Mz+s, where M is an integer and Isl a. Show that sinx=sgn(x)-(-1)-sins.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 74E
icon
Related questions
Question
To accurately approximate sinx and cos x for inclusion in a mathematical library, we first restrict their
domains. Given a real number x, divide by to obtain the relation
|x] =Mr+s, where M is an integer and Isl
a. Show that
sinx=sgn(x)-(-1)-sins.
b. Construct a rational approximation to sin s using n=m=4. Estimate the error when 0 < s <
x/2.
C.
Design an implementation of sin x using parts (a) and (b).
d. Repeat part (c) for cos x using the fact that cosx = sin(x+x/2).
Transcribed Image Text:To accurately approximate sinx and cos x for inclusion in a mathematical library, we first restrict their domains. Given a real number x, divide by to obtain the relation |x] =Mr+s, where M is an integer and Isl a. Show that sinx=sgn(x)-(-1)-sins. b. Construct a rational approximation to sin s using n=m=4. Estimate the error when 0 < s < x/2. C. Design an implementation of sin x using parts (a) and (b). d. Repeat part (c) for cos x using the fact that cosx = sin(x+x/2).
Expert Solution
steps

Step by step

Solved in 4 steps

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Functions and Change: A Modeling Approach to Coll…
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning